If x+1 over x=2 cosθ, then x³+1 over x³=?

If $x+{{1} \over x}=2$ cosθ, then $x^3+{{1} \over x^3}=?$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 2 cos 3θ.

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b) ---- (1)

Calculations:

Using equation (1), we get

⇒ (2cosθ)³ = x³ + 1/x³ + 3 × 2cosθ

⇒ 8 cos³θ = x³ + 1/x³ + 6cosθ

⇒ 8 cos³θ - 6cosθ = x³ + 1/x³

⇒ 2(4cos³θ - 3cosθ) = x³ + 1/x³

We know that, 4cos³θ - 3cosθ = cos3θ

⇒ x³ + 1/x³ = 2cos3θ

SSC CGL 2022 PYQ — Question 55